The Harmonic Oscillator, a Review of Classical and Elementary Quantum Mechanics

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

Guessing Harmonic Oscillator Wavefunctions Using Maple

The guessing of eigenfunctions is not trivial at higher quantum numbers, no matter what the system being considered. Instead of guessing, one can employ a symbolic calculus progam (Maple in this case) to aid in the reasoning process.

The Harmonic Oscillator's Frobenius Solution

The Frobenius solution to the differential equations associated with the harmonic oscillator (QM) is carried out in detail.

Advance P. Chem. Problems (I) Populations, Partition Functions, Particle in Box, Harmonic Oscillators, Angular Momentum and Rigid Rotor

This is a set of P. Chem. problems posed at slightly higher than the normal text book level, for students who are continuing in the study of this subject.

The Driven Harmonic Oscillator in Chemistry

The molecular dynamical simulation of the normal vibrational mode of water which involves H-O-H angle deformation, when driven by an external force, can be used to see how a driven harmonic oscillator, classically, is associated with the infra-red spectrum of water (and the absorption for this particular normal mode).

Molecular Dynamics and the Diatomic Molecule as Harmonic Oscillator and Rigid Rotor

The HCl molecule is simulated (using Maple) in its dynamics, for both vibrational (and implied) rotational motions. A discussion of the center of mass transformations involved is part of the total presentation.

The role of functional tumor suppressor 15-lipoxygenase 2 (15-LOX2) in normal human prostate epithelial cells and prostate cancer development

15-Lipoxygenase 2 (15-LOX2) is a recently cloned human lipoxygenase that shows tissue-restricted expression in prostate, lung, skin, and cornea. The protein level and enzymatic activity of 15-LOX2 have been shown to be down-regulated in prostate cancers compared with normal and benign prostate tissues. We report the cloning and functional characterization of 15-LOX2 and its three splice variants (termed 15-LOX2sv-a, 15-LOX2sv-b, and 15-LOX2sv-c) from primary prostate epithelial (NHP) cells. Western blotting with multiple NHP cell strains and prostate cancer (PCa) cell lines reveals that the expression of 15-LOX2 is lost in all PCa cell lines, accompanied by decreased enzymatic activity. 15-LOX2 is expressed at multiple subcellular locations, including cytoplasm, cytoskeleton, cell-cell border, and nucleus. Surprisingly, the three splice variants of 15-LOX2 are mostly excluded from the nucleus. To elucidate the relationship between nuclear localization, enzymatic activity, and tumor suppressive functions, we established PCa cell clones stably expressing 15-LOX2 or 15-LOX2sv-b. The 15-LOX2 clones express 15-LOX2 in the nuclei and possess robust enzymatic activity, whereas 15-LOX2sv-b clones show neither nuclear protein localization nor arachidonic acid-metabolizing activity. Interestingly, both 15-LOX2- and 15-LOX2sv-b-stable clones proliferate much slower in vitro when compared with control clones. When orthotopically implanted in nude mouse prostate, both 15-LOX2 and 15-LOX2sv-b suppress PC3 tumor growth in vivo. Finally, cultured NHP cells lose the expression of putative stem/progenitor cell markers, slow down in proliferation, and enter senescence. Several pieces of evidence implicate 15-LOX2 plays a role in replicative senescence of NHP cells: (1) promoter activity and the mRNA and protein levels of 15-LOX2 and its splice variants are upregulated in serially passaged NHP cells, which precede replicative senescence and occur in a cell-autonomous manner; (2) PCa cells stably expressing 15-LOX2 or 15-LOX2sv-b show a passage-related senescence-like phenotype; (3) enforced expression of 15-LOX2 or 15-LOX2sv-b in young NHP cells induce partial cell-cycle arrest and senescence-like phenotypes. Together, these results suggest that 15-LOX2 suppress prostate tumor development and do not necessarily depend on arachidonic acid-metabolizing activity and nuclear localization. Also, 15-LOX2 may serve as an endogenous prostate senescence gene and its tumor-suppressing functions might be associated with its ability to induce cell senescence. ^

Developmental programming of tumor suppressor gene penetrance

Epidemiological studies have led to the hypothesis that major risk factors for developing diseases such as hypertension, cardiovascular disease and adult-onset diabetes are established during development. This developmental programming hypothesis proposes that exposure to an adverse stimulus or insult at critical, sensitive periods of development can induce permanent alterations in normal physiological processes that lead to increased disease risk later in life. For cancer, inheritance of a tumor suppressor gene defect confers a high relative risk for disease development. However, these defects are rarely 100% penetrant. Traditionally, gene-environment interactions are thought to contribute to the penetrance of tumor suppressor gene defects by facilitating or inhibiting the acquisition of additional somatic mutations required for tumorigenesis. The studies presented herein identify developmental programming as a distinctive type of gene-environment interaction that can enhance the penetrance of a tumor suppressor gene defect in adult life. Using rats predisposed to uterine leiomyoma due to a germ-line defect in one allele of the tuberous sclerosis complex 2 (Tsc-2) tumor suppressor gene, these studies show that early-life exposure to the xenoestrogen, diethylstilbestrol (DES), during development of the uterus increased tumor incidence, multiplicity and size in genetically predisposed animals, but failed to induce tumors in wild-type rats. Uterine leiomyomas are ovarian-hormone dependent tumors that develop from the uterine myometrium. DES exposure was shown to developmentally program the myometrium, causing increased expression of estrogen-responsive genes prior to the onset of tumors. Loss of function of the normal Tsc-2 allele remained the rate-limiting event for tumorigenesis; however, tumors that developed in exposed animals displayed an enhanced proliferative response to ovarian steroid hormones relative to tumors that developed in unexposed animals. Furthermore, the studies presented herein identify developmental periods during which target tissues are maximally susceptible to developmental programming. These data suggest that exposure to environmental factors during critical periods of development can permanently alter normal physiological tissue responses and thus lead to increased disease risk in genetically susceptible individuals. ^

Oncogenic activation of c-Abl tyrosine kinase in non-small cell lung cancer: FUS1 tumor suppressor down-regulates c-Abl tyrosine kinase

The FUS1 tumor suppressor gene (TSG) has been found to be deficient in many human non-small cell lung cancer (NSCLC) tissue samples and cell lines (1,2,3). Studies have shown potent anti-tumor activity of FUS1 in animal models where FUS1 was delivered through a liposomal vector (4) and the use of FUS1 as a therapeutic agent is currently being studied in clinical human trials (5). Currently, the mechanisms of FUS1 activity are being investigated and my studies have shown that c-Abl tyrosine kinase is inhibited by the FUS1 TSG.^ Considering that many NSCLC cell lines are FUS1 deficient, my studies further identified that FUS1 deficient NSCLC cells have an activated c-Abl tyrosine kinase. C-Abl is a known proto-oncogene and while c-Abl kinase is tightly regulated in normal cells, constitutively active Abl kinase is known to contribute to the oncogenic phenotype in some types of hematopoietic cancers. My studies show that the active c-Abl kinase contributes to the oncogenicity of NSCLC cells, particularly in tumors that are deficient in FUS1, and that c-Abl may prove to be a viable target in NSCLC therapy.^ Current studies have shown that growth factor receptors play a role in NSCLC. Over-expression of the epidermal growth factor receptor (EGFR) plays a significant role in aggressiveness of NSCLC. Current late stage treatments include EFGR tyrosine kinase inhibitors or EGFR antibodies. Platelet-derived growth factor receptor (PDGFR) also has been shown to play a role in NSCLC. Of note, both growth factor receptors are known upstream activators of c-Abl kinase. My studies indicate that growth factor receptor simulation along deficiency in FUS1 expression contributes to the activation of c-Abl kinase in NSCLC cells. ^

Alterations in cell adhesion and migration are transcriptionally regulated by the tumor suppressor, TP53

The p53 transcription factor is a tumor suppressor and a master regulator of apoptosis and the cell cycle in response to cell stress. In some advanced tumors, such as prostate cancers, the loss of p53 correlates with an increase in the occurrence of metastases. In addition, several groups have suggested that p53 status correlates with changes in cell migration and cell morphology associated with a migratory phenotype. Others have identified several genes with roles in cell migration that are directly transcriptionally regulated by p53. Even so, modulation of cell migration is not widely recognized as a p53 stress response. ^ In an effort to identify novel p53 target genes and expand our knowledge of the p53 transcriptional response, we performed Affymetrix gene expression analysis in p53-null PC3 prostate cancer cells following infection with a control virus or adenoviral construct expressing wild-type p53. Over 300 genes that had not been previously recognized as p53 target genes were identified. Of these genes, 224 were upregulated and 111 were downregulated (p<0.05). Functional over-representation analysis identified cell migration as a significantly over-represented biological function of p53. Further analysis identified two genes that are critical for the control of cell migration as potential p53 targets. One, hyaluronan mediated motility receptor (HMMR), has recently been shown to be a p53 target important for regulation of the cell cycle. Here, we show that HMMR is downregulated by p53 in several cell lines, and HMMR's regulation is dependent on the presence of the cdk inhibitor, p21, and histone deactelyase activity. The other gene, carcinoembryonic antigen-related cell adhesion molecule 1 (CEACAM1), itself a tumor suppressor, is shown here, for the first time, as a p53 direct target by ChIP analysis. We next determined the effect of p53 activation on cell migration and found that p53 significantly slows the rate of cell migration in Boyden chamber migration assays and digital videomicroscopy wound healing studies. Further, our studies established the specific roles of CEACAM1 and HMMR in cell migration and determine that loss of CEACAM1 and overexpression of HMMR independently contribute to increased cell migration. Taken together, these studies provide a direct mechanistic link between p53 to the regulatory control of specific target genes that mediate cell adhesion and migration. ^

Transcriptional regulation of lung tumor suppressor GPRC5A in malignant and normal cells

Chronic exposure of the airways to cigarette smoke induces inflammatory response and genomic instability that play important roles in lung cancer development. Nuclear factor kappa B (NF-κB), the major intracellular mediator of inflammatory signals, is frequently activated in preneoplastic and malignant lung lesions. ^ Previously, we had shown that a lung tumor suppressor GPRC5A is frequently repressed in human non-small cell lung cancers (NSCLC) cells and lung tumor specimens. Recently, other groups have shown that human GPRC5A transcript levels are higher in bronchial samples of former than of current smokers. These results suggested that smoking represses GPRC5A expression and thus promotes the occurrence of lung cancer. We hypothesized that cigarette smoking or associated inflammatory response repressed GPRC5A expression through NF-κB signaling. ^ To determine the effect of inflammation, we examined GPRC5A protein expression in several lung cell lines following by TNF-α treatment. TNF-α significantly suppressed GPRC5A expression in normal small airway epithelial cells (SAEC) as well as in Calu-1 cells. Real-time PCR analysis indicated that TNF-α inhibits GPRC5A expression at the transcriptional level. NF-κB, the major downstream effectors of TNF-α signaling, mediates TNF-α-induced repression of GPRC5A because over-expression of NF-κB suppressed GPRC5A. To determine the region in the GPRC5A promoter through which NF-κB acts, we examined the ability of TNF-α to inhibit a series of reporter constructs with different deletions of GPRC5A promoter. The luciferase assay showed that the potential NF-κB binding sites containing region are irresponsible for TNF-α-induced suppression. Further analysis using constructs with different deletions in p65 revealed that NF-κB-mediated repression of GPRC5A is transcription-independent. Co-immunoprecipitation assays revealed that NF-κB could form a complex with RAR/RXR heterodimer. Moreover, the inhibitory effect of NF-κB has been found to be proportional to NF-κB/RAR ratio in luciferase assay. Finally, Chromatin IP demonstrated that NF-κB/p65 bound to GPRC5A promoter as well as RAR/RXR and suppressed transcription. Taken together, we propose that inflammation-induced NF-κB activation disrupts the RA signaling and suppresses GPRC5A expression and thus contributes to the oncogenesis of lung cancer. Our studies shed new light on the pathogenesis of lung cancer and potentially provide novel interventions for preventing and treating this disease. ^

Regulation of estrogen receptor alpha by the tumor suppressor p53 in breast cancer cells

Estrogen receptor (ER) and the tumor suppressor p53 are key prognostic indicators in breast cancer. Estrogen signaling through its receptor (ER) controls proliferation of normal as well as transformed mammary epithelial cells, and the presence of ER is established as a marker of good prognosis and response to therapy. The p53 tumor suppressor gene is often referred to as the "cellular gatekeeper" due to its extensive control of cell proliferation and apoptosis. Loss of functional p53 is a negative prognostic indicator and is correlated with lack of response to antiestrogens, reduced disease-free interval and increased chance of disease recurrence. Clinical studies have demonstrated that tumors with mutated p53 tend to be ER negative, while ER positive tumors tend to have wild type p53. ^ Recent studies from our lab indicate that p53 genotype correlates with estrogen receptor expression in mammary tumors in vivo. We therefore hypothesized that p53 regulates ER expression in mammary cancer cells by recruitment of specific cofactors to the ER promoter. To test this, MCF-7 cells were treated with doxorubicin or ionizing radiation, both of which stimulated significant increases in p53 expression, as expected, but also increased ER expression in a p53-dependent manner. Furthermore, in cells treated with siRNA targeting p53, both p53 and ER protein levels were significantly reduced. P53 was also demonstrated to transcriptionally regulate the ER promoter in luciferase assays and chromatin immunoprecipitation assays showed that p53 was recruited to the ER promoter along with CARM1, CBP, c-Jun and Sp1 and that this multifactor complex was formed in a p53-dependent manner. The regulation of ER by p53 has therapeutic implications, as the treatment of breast cancer cells with doxorubicin sensitized these cells to tamoxifen treatment. Furthermore, response to tamoxifen as well as to estrogen was dependent on p53 expression in ER positive human breast cancer cells. Taken together, these data demonstrate that p53 regulates ER expression through transcriptional control of the ER promoter, accounting for their concordant expression in human breast cancer and identifying potentially beneficial therapeutic strategies for the treatment of ER positive breast cancers. ^

14-3-3 ZETA OVEREXPRESSION SERVES AS A NOVEL MOLECULAR SWITCH TURNING TGF-BETA FROM TUMOR SUPPRESSOR TO TUMOR PROMOTER

TGF-β plays an important role in differentiation and tissue morphogenesis as well as cancer progression. However, the role of TGF-β in cancer is complicate. TGF-β has primarily been recognized as tumor suppressor, because it can directly inhibit cell proliferation of normal and premalignant epithelial cell. However, in the last stage of tumor progression, TGF-β functions as tumor promoter to enhance tumor cells metastatic dissemination and expands metastatic colonies. Currently, the mechanism of how TGF-β switches its role from tumor suppressor to promoter still remains elusive. Here we identify that overexpression of 14-3-3ζ inhibits TGF-β’s cell cytostatic program through destabilizing p53 in non-transformed human mammary epithelial cells. Mechanistically, we found that 14-3-3ζ overexpression leads to 14-3-3σ downregulation, thereby activates PI3K/Akt signaling pathway and degrades p53, and further inhibits TGF-β induced p21 expression and cell cytostatic function. In addition, we found that overexpression of 14-3-3ζ promotes TGF-β induced breast cancer cells bone metastatic colonization through stabilizing Gli2, which is an important co-transcriptional factor for p-smad2 to activate PTHrP expression and bone osteolytic effect. Taken together, we reveal a novel mechanism that 14-3-3ζ dictates the tumor suppressor or metastases promoter activities of TGF-β signaling pathway through switching p-smad2 binding partner from p53 to Gli2. The expected results will not only provide us the better understanding of the important role of 14-3-3ζ in the early stage of breast cancer development, but also deeply impact our knowledge of signaling mechanisms underlying the complex roles of TGF-β in cancer, which will give us a more accurate strategy to determine when and how anti-TGF-β targeted therapy might be effective.

A Genomic Approach to Identify The Notch Pathway as a Putative Tumor Suppressor in Endometrial Cancer

Endometrial cancer is the most common gynecological malignancy and the fourth most frequently diagnosed cancer among women. The molecular changes that distinguish normal endometrium from endometrial carcinoma are not thoroughly understood. Identification of these changes could potentially aid in identifying at-risk women who are especially prone to develop endometrial cancer, such as obese women and women with Lynch Syndrome. A microarray analysis was performed using normal endometrium from thin and obese women and cancerous endometrium from obese women. We validated the differential expression of ten genes whose expression was significantly up-regulated or down-regulated using qRT-PCR. All of the genes had distinct expression levels depending on the endometrial carcinoma histotype. As a result, they could serve as molecular markers to distinguish between normal endometrium and endometrial cancer, as well as between low grade endometrial carcinomas and high grade endometrial carcinomas. Two of the ten genes validated, HEYL and HES1, are down-stream targets of the Notch signaling pathway. HEYL and HES1 were identified by microarray and qRT-PCR to have a significant decrease in expression in endometrial carcinomas compared to normal endometrium. We further analyzed the differential expression of other components of the Notch signaling pathway, Notch4 and Jagged1. They were also identified by qRT-PCR to be significantly down-regulated in endometrial carcinomas compared to normal endometrium. Therefore, we believe the Notch signaling pathway to act as a tumor suppressor in endometrial carcinomas.

The role of suppressor factors in the regulation of immune responses by ultraviolet radiation -induced suppressor T lymphocytes

The purpose of these studies was to determine the role of suppressor factors (TsF) in the regulation of immune responses by ultraviolet radiation-induced suppressor T lymphocytes (Ts). The Ts were induced following epicutaneous sensitization with contact allergens to an unirradiated site on mice irradiated five days earlier with 40 kJ/m$\sp2$ UVB (280-320 nm) radiation. The spleens of such mice contain afferent, hapten-specific, Thy-1$\sp+$, Lyt-1$\sp+$,2$\sp-$ Ts that suppress in vivo contact hypersensitivity (CHS) and antibody responses and the in vitro generation of cytotoxic T lymphocytes (CTL). Four approaches were used to determine the role of TsF. First, lysates produced from sonically-disrupted Ts were injected i.v. into normal animals; they inhibited CHS in vivo in a nonspecific manner. The lysates suppressed the induction and elicitation of CHS, and they inhibited the in vitro generation of CTL. Lysates prepared from splenocytes obtained from unirradiated mice or UV-irradiated, unsensitized mice failed to inhibit either response. Second, supernatants from cultures containing Ts, normal syngeneic responder lymphocytes, and hapten-modified stimulator cells were injected i.v. into normal recipients. They inhibited the induction of CHS and did so in a hapten-specific manner. Cellular and kinetic requirements were observed for the generation of suppressive activity. Splenocytes from mice treated with Ts supernatants suppressed CHS when transferred into normal animals. The supernatants also suppressed the in vitro generation of specific CTL. Third, the TsF-specific B16G monoclonal antibody was tested for its ability to modulate the effects of UV radiation in vivo. The i.v. injection of B16G into UV-irradiated mice reduced the suppression of CHS. Splenocytes of B16G-treated mice transferred into normal recipients, and they suppressed CHS, indicating that the Ts were not depleted. Fourth, B16G was used to isolate a putative TsF by antibody immunoadsorbance. When the B16G-bound fraction was eluted and injected i.v. into normal animals, it suppressed CHS and represented a 900-fold enrichment of activity over the starting material, based on specific activity. By SDS-PAGE, the B16G-bound material contained nondisulfide-linked 45- and 50-kDa components. These results suggest that TsF may play an immunoregulatory role in CHS. The isolation of a UV radiation-induced TsF lends credence to the involvement of such molecules. ^